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Search: id:A081421
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| A081421 |
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Quotient after one division by 2 of numbers of the form 3^(2n) + 5^(2n). |
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+0
1
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| 1, 17, 353, 8177, 198593, 4912337, 122336033, 3054149297, 76315468673, 1907542343057, 47685459212513, 1192108586037617, 29802463602463553, 745059330625296977, 18626462930705797793, 465661390253305305137
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Except for the first term, these numbers always end in 3 and 7 and necessarily generate an odd number as the quotient upon a single division by 2. Indeed for even n, 3^n+5^n can be written as (4-1)^n + (4+1)^n = 4h+1 + 4i+1 for some h,i. Then we add and get 4(h+i)+2. Divide by 2 to get 2(h+i) + 1 and odd number.
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PROGRAM
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(PARI) p3np5n(n) = { forstep(x=0, n, 2, y = (3^x + 5^x)/2; print1(y" ") ) }
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CROSSREFS
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Sequence in context: A009046 A012112 A137246 this_sequence A121824 A120287 A002197
Adjacent sequences: A081418 A081419 A081420 this_sequence A081422 A081423 A081424
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Apr 20 2003
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